Theory of the Aberration of Light. 81 



sin \t>' = sin <p' 4? cos <P' cos (<?' + a )- 



On substituting these values in equations (A), and observing 

 that in the terms multiplied by q we may put <p, = <p, jw. sin <p' 

 = sin <p, the small terms destroy each other, and we have 

 sin <p t — sin <p, jw, sin <p' = sin <p . Hence the laws of reflexion 

 and refraction at the surface of a refracting medium will not 

 be affected by the motion of the aether. 



In the preceding investigation it has been supposed that 

 the refraction is out of vacuum into a refracting medium. 

 But the result is the same in the general case of refraction out 

 of one medium into another, and reflexion at the common 

 surface. For all the preceding reasoning applies to this case 



if we merely substitute -^, -~- 2 for p, q, — for V, and ~ for p, 



p! being the refractive index of the first medium. Of course 

 refraction out of a medium into vacuum is included as a par- 

 ticular case. 



It follows from the theory just explained, that the light 

 coming from any star will behave in all cases of reflexion and 

 ordinary refraction precisely as it would if the star were situ- 

 ated in the place which it appears to occupy in consequence 

 of aberration, and the earth were at rest. It is, of course, 

 immaterial whether the star is observed with an ordinary tele- 

 scope, or with a telescope having its tube filled with fluid. It 

 follows also that terrestrial objects are referred to their true 

 places. All these results would follow immediately from the 

 theory of aberration which I proposed in the July number of 

 this Magazine ; nor have I been able to obtain any result, ad- 

 mitting of being compared with experiment, which would be 

 different according to which theory we adopted. This affords 

 a curious instance of two totally different theories running par- 

 allel to each other in the explanation of phaenomena. I do 

 not suppose that many would be disposed to maintain Fres- 

 nel's theory, when it is shown that it may be dispensed with, 

 inasmuch as we would not be disposed to believe, without 

 good evidence, that the aether moved quite freely through the 

 solid mass of the earth. Still it would have been satisfactory, 

 if it had been possible, to have put the two theories to the test 

 of some decisive experiment. 



